Theorem equncomi 3253

Description: Inference form of equncom 3252. (Contributed by Alan Sare, 18-Feb-2012.)

Hypothesis

Ref	Expression
equncomi.1	|- A = ( B u. C )

Assertion

Ref	Expression
equncomi	|- A = ( C u. B )

Proof of Theorem equncomi

Step	Hyp	Ref	Expression
1		equncomi.1	. 2 |- A = ( B u. C )
2		equncom 3252	. 2 |- ( A = ( B u. C ) <-> A = ( C u. B ) )
3	1, 2	mpbi 144	1 |- A = ( C u. B )

Syntax hints:   = wceq 1335   u. cun 3100

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139

This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-un 3106

This theorem is referenced by:  disjssun  3457  difprsn1  3695  unidmrn  5118  phplem1  6797  djucomen  7151